...us at this point, then the subdifferential is non-empty and compact in the topology $ \sigma ( Y, X) $.
that is compact in the topology $ \sigma ( Y, X) $
3 KB (480 words) - 14:55, 7 June 2020
$#C+1 = 49 : ~/encyclopedia/old_files/data/S090/S.0900610 Strong topology
The [[Weak topology|weak topology]] on $ L $
3 KB (419 words) - 08:24, 6 June 2020
A concept in measure theory, determined by a certain topology in a space of measures that are defined on a certain [[Algebra of sets|σ-a
===The norm or [[strong topology]]===
9 KB (1,371 words) - 08:33, 16 August 2013
...e often used: the strong topology determined by this norm and the weak-$*$-topology.
...uses the term dual space. The weak-$*$-topology on $E^{*}$ is the weakest topology on $E^{*}$ for which all the evaluation mappings $f\mapsto f(x)$, $f\in E^{
1 KB (186 words) - 18:01, 30 November 2012
...space]] which is boundedly compact (in itself) in the weak (resp. strong) topology is [[Reflexive space|reflexive]] (resp. a [[Montel space]]). A normed space
1 KB (200 words) - 17:07, 17 October 2014
$#C+1 = 64 : ~/encyclopedia/old_files/data/O068/O.0608410 Operator topology
A topology on the space $ L( E, F ) $
5 KB (737 words) - 08:04, 6 June 2020
that are continuous in the weak topology of $ U $;
cf. [[Weak topology|Weak topology]]); and let the set $ X = \{ {x } : {f _ {i} ( x) \geq 0, i = 1 \dots m
6 KB (879 words) - 19:35, 12 January 2024
...mplete Mackey space and the space dual to $E$ equipped with the strong $E$-topology is semi-reflexive, then $E$ is reflexive.
3 KB (444 words) - 19:36, 11 October 2023
The [[locally convex topology]] on a vector space $X$ generated by the family of [[semi-norm]]s $p(x)=|f(
...y as introduced above is often denoted by $\sigma(X,F)$. It is a Hausdorff topology if and only if $F$ is a [[total set]], that is, separates the points of $X$
1 KB (150 words) - 22:17, 10 December 2016
...a complete set in the weak topology will be a complete set in the initial topology also.
1 KB (254 words) - 09:44, 5 August 2014
...$X$ that is homeomorphic to a subset of a [[Banach space]] with the [[weak topology]] [[#References|[a3]]].
...a subset of $c_0(I)$ in the weak topology (or, equivalently, the pointwise topology), for some set $I$; and iii) $X$ has a family $\mathcal{B} = \cup_{n<\omega
2 KB (383 words) - 17:56, 31 December 2017
$#C+1 = 38 : ~/encyclopedia/old_files/data/V096/V.0906000 Vague topology
...sets|Borel field of sets]]), generated by the (set of open subsets of the) topology of $ X $.
3 KB (507 words) - 19:20, 1 January 2021
...s is equivalent to the space being Lindelöf. If a Banach space in the weak topology is topologically generated by some compactum lying within it, then it is pa
...="top"> A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) (Translated from Russian)</TD></
9 KB (1,401 words) - 14:04, 30 July 2014
formed by the continuous functions and endowed with the following Hausdorff topology: a fundamental system of neighbourhoods of zero in $ X $
to be a (topologically-) free set in the weak topology $ \sigma ( X, X ^ {*} ) $
3 KB (399 words) - 19:40, 5 June 2020
...mages/t/t093/t093470/t0934705.png" /> is considered with the weak operator topology. The concept of a totally-irreducible set, initially introduced for Banach
8 KB (1,059 words) - 17:18, 7 February 2011
...] is bounded in the [[strong topology]] and relatively compact in the weak topology.
...ment that the dual of a barrelled space is quasi-complete for any $\sigma$-topology. (For the last notion see [[Topological vector space]]; [[Space of mappings
3 KB (507 words) - 13:44, 17 March 2023
...rongly exposed points, [[#References|[a2]]] (cf. also [[Weak topology|Weak topology]]). R.E. Huff and P.D. Morris [[#References|[a7]]] showed that this propert
...="top"> M.J. Fabian, "Gâteaux differentiability of convex functions and topology-weak Asplund spaces" , Wiley (1997)</td></tr></table>
6 KB (893 words) - 16:59, 1 July 2020
In [[metric space]]s and [[Banach space]]s with the [[weak topology]] the notions of compactness, sequential compactness and countable compactn
...="top"> A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) (Translated from Russian)</TD></
1 KB (207 words) - 20:42, 2 November 2014
...p"> K. Kunen, "Weak $P$-points in $\mathbf{N}^*$" Á. Császár (ed.) , ''Topology (Proc. Fourth Colloq., Budapest, 1978)'' , '''II''' , North-Holland (1980)
3 KB (409 words) - 20:01, 21 November 2017
$#C+1 = 27 : ~/encyclopedia/old_files/data/S110/S.1100200 Skorokhod topology
A [[Topological structure (topology)|topological structure (topology)]] on the space $ D [ 0,1 ] $
4 KB (518 words) - 08:14, 6 June 2020